Control of calcium oscillations by membrane fluxes
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR. The units have been checked and they are consistent. Note that the published paper alone does not contain the full set of equations required to describe the complete model. As stated in the paper, certain equtions were taken from a previously published model (Sneyd and Dufour, 2002, also available as a CellML model). Where initial conditions were not defined in the paper, arbitary values were used to complete the CellML model description (for c, ce, R, O, I_1, I_2, S and A). The CellML model output looks reasonable, with Calcium oscillations generated, however it is likely the output does not perfectly match the published model description. There are no published figures of changing calcium concentration agaisnt time so we cannot confirm the accuracy of the CellML model.
Model Structure
ABSTRACT: It is known that Ca(2+) influx plays an important role in the modulation of inositol trisphosphate-generated Ca(2+) oscillations, but controversy over the mechanisms underlying these effects exists. In addition, the effects of blocking membrane transport or reducing Ca(2+) entry vary from one cell type to another; in some cell types oscillations persist in the absence of Ca(2+) entry (although their frequency is affected), whereas in other cell types oscillations depend on Ca(2+) entry. We present theoretical and experimental evidence that membrane transport can control oscillations by controlling the total amount of Ca(2+) in the cell (the Ca(2+) load). Our model predicts that the cell can be balanced at a point where small changes in the Ca(2+) load can move the cell into or out of oscillatory regions, resulting in the appearance or disappearance of oscillations. Our theoretical predictions are verified by experimental results from HEK293 cells. We predict that the role of Ca(2+) influx during an oscillation is to replenish the Ca(2+) load of the cell. Despite this prediction, even during the peak of an oscillation the cell or the endoplasmic reticulum may not be measurably depleted of Ca(2+).
The original paper reference is cited below:
Control of calcium oscillations by membrane fluxes, J. Sneyd, K. Tsaneva-Atanasova, D. I. Yule, J. L. Thompson, and T. J. Shuttleworth, 2004, PNAS, 101, 1392-1396. PubMed ID: 14734814
cell diagram
Schematic diagram of the calcium fluxes described by the mathematical model.
$\frac{d c}{d \mathrm{time}}=\mathrm{J\_IPR}-\mathrm{J\_serca}+\mathrm{delta}(\mathrm{J\_in}-\mathrm{J\_pm})$
$\frac{d \mathrm{ce}}{d \mathrm{time}}=\mathrm{gamma}(\mathrm{J\_serca}-\mathrm{J\_IPR})$
$\mathrm{J\_IPR}=(\mathrm{kf}(0.1O+0.9A)^{4.0}+\mathrm{g1})(\mathrm{ce}-c)$
$\frac{d R}{d \mathrm{time}}=\mathrm{phi\_2\_}O-\mathrm{phi\_2}pR+\mathrm{phi\_1}R+(\mathrm{l\_2\_}+\mathrm{k\_1\_})\mathrm{I\_1}$
$\frac{d O}{d \mathrm{time}}=\mathrm{phi\_2}pR-(\mathrm{phi\_2\_}+\mathrm{phi\_4}+1\mathrm{phi\_3})O+\mathrm{phi\_4\_}A+\mathrm{k\_3\_}S$
$\frac{d \mathrm{I\_1}}{d \mathrm{time}}=\mathrm{phi\_1}R-(\mathrm{k\_1\_}+\mathrm{l\_2\_})\mathrm{I\_1}$
$\frac{d \mathrm{I\_2}}{d \mathrm{time}}=\mathrm{phi\_5}A-(\mathrm{k\_1\_}+\mathrm{l\_2\_})\mathrm{I\_2}$
$\frac{d S}{d \mathrm{time}}=1\mathrm{phi\_3}O-\mathrm{k\_3\_}S$
$\frac{d A}{d \mathrm{time}}=\mathrm{phi\_4}O-\mathrm{phi\_4\_}A+\mathrm{phi\_5}A+(\mathrm{k\_1\_}+\mathrm{l\_2\_})\mathrm{I\_2}$
$\mathrm{phi\_1}=\frac{(\mathrm{k\_1}\mathrm{L\_1}+\mathrm{l\_2})c}{\mathrm{L\_1}+c(1.0+\frac{\mathrm{L\_1}}{\mathrm{L\_3}})}\mathrm{phi\_2}=\frac{\mathrm{k\_2}\mathrm{L\_3}+\mathrm{l\_4}c}{\mathrm{L\_3}+c(1.0+\frac{\mathrm{L\_3}}{\mathrm{L\_1}})}\mathrm{phi\_2\_}=\frac{\mathrm{k\_2\_}+\mathrm{l\_4\_}c}{1.0+\frac{c}{\mathrm{L\_5}}}\mathrm{phi\_3}=\frac{\mathrm{k\_3}\mathrm{L\_5}}{c+\mathrm{L\_5}}\mathrm{phi\_4}=\frac{(\mathrm{k\_4}\mathrm{L\_5}+\mathrm{l\_6})c}{c+\mathrm{L\_5}}\mathrm{phi\_4\_}=\frac{\mathrm{L\_1}(\mathrm{k\_4\_}+\mathrm{l\_6\_})}{c+\mathrm{L\_1}}\mathrm{phi\_5}=\frac{(\mathrm{k\_1}\mathrm{L\_1}+\mathrm{l\_2})c}{c+\mathrm{L\_1}}$
$\mathrm{J\_serca}=\frac{\mathrm{Vs}c}{\mathrm{Ks}+c}\frac{1.0}{\mathrm{ce}}$
$\mathrm{J\_pm}=\frac{\mathrm{Vp}c^{2.0}}{\mathrm{Kp}^{2.0}+c^{2.0}}$
$\mathrm{J\_in}=\mathrm{alpha1}+\mathrm{alpha2}p$
calcium dynamics
oscillator
IP3 receptor
receptor
R
shut state
S
calcium extrusion across the plasma membrane
J_pm
14734814
Control of calcium oscillations by membrane fluxes
101
1392
1396
The University of Auckland
Auckland Bioengineering Institute
keyword
active state
A
open state
O
Catherine Lloyd
IP3 concentration
p
2004-02-03
calcium release through the IPR
J_IPR
Catherine
Lloyd
May
cytosolic calcium
c
calcium pumping into the ER
J_serca
J
Thompson
L
inactive state 1
I_1
2004-06-13
ER calcium
ce
inactive state 2
I_2
calcium entry
J_in
K
Tsaneva-Atanasova
Auckland Bioengineering Institute, The University of Auckland
Sneyd et al.'s 2004 mathematical model for Ca2+ oscillations and their control by membrane fluxes.
T
Shuttleworth
J
D
Yule
I
c.lloyd@auckland.ac.nz
James
Sneyd
This is the CellML description of Sneyd et al.'s 2004 mathematical model for Ca2+ oscillations and their control by membrane fluxes.
PNAS